Effects Of Mean Shear Research Articles

Reynolds number dependence of the turbulent/non-turbulent interface in temporally developing turbulent boundary layers

Direct numerical simulations (DNS) of temporally developing turbulent boundary layers are performed with a wide range of Reynolds numbers based on the momentum thickness $Re_{\theta } = 2000$ – $13\,000$ for investigating the Reynolds number dependence of the turbulent/non-turbulent interface (TNTI) layer. The grid spacing in the DNS is determined carefully such that small-scale turbulent motions near the TNTI are well resolved. The outer edge of the TNTI layer, called the irrotational boundary, is detected with vorticity magnitude. The mean thicknesses of the TNTI layer, $\delta _{TNTI}$ , turbulent sublayer, $\delta _{TSL}$ , and viscous superlayer, $\delta _{VSL}$ , are found to be approximately $15\eta _{TI}$ , $10\eta _{TI}$ and $5\eta _{TI}$ , respectively, where $\eta _{TI}$ is the Kolmogorov scale taken in the turbulent region near the TNTI layer. The mean curvature of the irrotational boundary is also characterized by $\eta _{TI}$ . The shear parameter and the shear-to-vorticity ratio show that the mean shear effects near the TNTI layer are not significant for both large and small scales. The anisotropy tensors of Reynolds stress and vorticity suggest that the turbulence under the TNTI layer tends to be isotropic at high $Re_{\theta }$ , for which $\eta _{TI}/\delta \sim Re_{\theta }^{-3/4}$ is valid with the boundary layer thickness $\delta$ . The surface area of the irrotational boundary is consistent with the fractal analysis of the interface, where the fractal dimension $D_f$ is found to be $2.14$ – $2.20$ . The present results suggest that the mean entrainment rate per unit horizontal area normalized by the friction velocity varies slowly as $Re_{\theta }^{(3/4)(D_f-2)}$ for $Re_{\theta } \geq 4000$ .

Effects of mean shear on the vortex identification and the orientation statistics

This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incompressible turbulent channel flows. It is concluded that the difference in the swirling strength for vortex identification is minimal in the logarithmic region such that these two situations share the same threshold. Regarding the vortex orientation, the inclination angle remains similar. However, as the wall-normal distance increases, a more and more obvious distinction is noticed for its orientation with respect to the spanwise (z) direction. It is mainly due to their intrinsic differences and attendant contrasting preference for the vortex identification, i.e., vortices rotating in the −z direction for the total velocity field and in the z direction for the fluctuating one. These observations function as a reasonable explanation for various remarks in previous studies.

Revised mixing coefficient scaling for sheared stably stratified turbulence

We revisit and extend the turbulent Froude number ( $Fr_k$ ) scaling for the mixing coefficient ( $\varGamma$ ) introduced by Garanaik & Venayagamoorthy (GV) (J. Fluid Mech., vol. 867, 2019, pp. 323–333) by directly incorporating the effects of mean shear through the non-dimensional shear parameter $S_{\ast } = S k/\epsilon _k$ . For flows where the effects of mean shear are stronger than the background vertical stratification, we find $\varGamma \sim Fr_k^{-2} S_\ast ^{-1}$ for weakly stratified sheared turbulence and $\varGamma \sim Fr_k^{-1}S_\ast ^{-1}$ for moderately stratified sheared turbulence. The scaling procedure is inconclusive for strongly stratified sheared turbulence, but using two independent datasets of homogeneous, sheared, stably stratified turbulence, we empirically observe $\varGamma \sim Fr_k^{-0.5} S_\ast ^{-1}$ . Our revised scaling better collapses both datasets compared with the original GV scaling, and we note that the moderately stratified sheared regime is extremely narrow (or maybe even non-existent). We also apply our scaling to the time-varying open channel simulations of Issaev et al. (J. Fluid Mech., vol. 935, 2022) and observe $\varGamma \sim Fr_k^{-2}S_\ast ^{-1}$ for weakly stratified sheared turbulence, but we observe deviations from our revised scaling for moderate and strong stratifications due to time-varying mean shear and vertical transport. Finally, we apply our revised scaling to field measurements of Conry, Kit & Fernando (Environ. Fluid Mech., vol. 20, 2020, pp. 1177–1197) and observe $\varGamma \sim Fr_k^{-2} S_\ast ^{-1}$ . We emphasize that our revised scaling is applicable only for stably stratified, vertically sheared turbulence with weak spatio-temporal variations of the mean shear and stratification, and we expect different scaling to apply when additional effects such as depth-varying radiative heating/cooling are present or when the orientation of the mean shear relative to the gravity vector is modified (e.g. horizontal shear).

Vertical confinement effects on a fully developed turbulent shear layer

The effects of vertical confinement on a turbulent shear layer are investigated with large-eddy simulations of a freely developing shear layer (FSL) and a wall-confined shear layer (WSL) that develops between two horizontal walls. In the case of the WSL, the growth of the shear layer is inhibited by the walls. Once the walls prevent the development of the shear layer, highly anisotropic velocity fluctuations become prominent in the flow. These anisotropic velocity fluctuations are recognized as elongated large-scale structures (ELSS), whose streamwise length is much larger than the length scales in the other directions. Spectral analysis confirms that the turbulent kinetic energy is dominated by the ELSS, whose streamwise length grows continuously. A proper orthogonal decomposition can effectively extract a velocity component associated with the ELSS. The isotropy of the Reynolds stress tensor is changed by the presence of the ELSS. These changes in flow characteristics due to the ELSS are not observed in the FSL, where the shear layer thickness increases continuously. These behaviors of the WSL are consistent with those of stably stratified shear layers (SSSLs), where flow structures similar to ELSS also develop when the vertical flow development is confined by the stable stratification. The vertical confinement by the walls or stable stratification strengthens mean shear effects. The flow behavior at large scales in the WSL and SSSL is consistent with rapid distortion theory for turbulence subject to mean shear, suggesting that the development of ELSS is caused by the mean shear.

Approach to the 4/3 law for turbulent pipe and channel flows examined through a reformulated scale-by-scale energy budget

In this study, we propose a scale-by-scale (SBS) energy budget equation for flows with homogeneity in at least one direction. This SBS budget represents a modified form of the equation first proposed by Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87–109) for the channel centreline – the primary difference is that, here, we consider the role of pressure along with the errors associated with the isotropic approximations of the interscale divergence and Laplacian of the squared velocity increment. The term encompassing the effects of mean shear is also characterised such that the present analysis can be extended straightforwardly to locations away from the centreline. We show, based on a detailed analysis of previously published channel flow direct numerical simulations and pipe flow experiments near the centreline, how several terms in the present SBS budget equation (including the third-order velocity structure function) behave with increasing Reynolds number. The behaviour of these terms is shown to imply a rate of emergence and subsequent growth of the 4/3 law scale subrange at the channel centreline and pipe axis. The analysis also suggests that the peak magnitude of the third-order velocity structure function occurs at a scale that is fixed in proportion to the Taylor microscale at sufficiently high Reynolds number.

A modification of Matake criterion for considering the effect of mean shear stress under high cycle fatigue loading

AbstractIn the present paper, a brief review for some existing critical plane‐based life prediction models is presented, and limitations of these models in reflecting the influence of mean stress on fatigue life are discussed. It is found that the effect of mean normal stress on fatigue damage has been well taken into account for most of the critical plane‐based fatigue life prediction models, while mean shear stress effect is not well considered in these models. Therefore, a new critical plane‐based multiaxial high cycle fatigue life prediction model is proposed in this paper to account for the effects of both mean shear and normal stresses. The shear Walker factor and mean normal stress sensitivity index are introduced in the developed criterion to consider the effects of mean shear and normal stresses, respectively. Procedures to determine the damage parameters acting on the critical plane and to calculate the material constants contained in the proposed model are all presented. Experimental validations by using six different materials show that most of the predictions are within a factor of 3 in fatigue life.

Quantifying Residual, Eddy, and Mean Flow Effects on Mixing in an Idealized Circumpolar Current

AbstractMeridional diffusivity is assessed for a baroclinically unstable jet in a high-latitude idealized circumpolar current (ICC) using the Model for Prediction across Scales Ocean (MPAS-O) and the online Lagrangian in Situ Global High-Performance Particle Tracking (LIGHT) diagnostic via space–time dispersion of particle clusters over 120 monthly realizations of O(106) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000) m2 s−1 and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100) m2 s−1 because of the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥80% of the total diffusivity relative to mean shear [O(100) m2 s−1], linear waves [O(1000) m2 s−1], and undecomposed full diffusivity [O(6000) m2 s−1]. Diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.

Experimental investigation of the effects of mean shear and scalar initial length scale on three-scalar mixing in turbulent coaxial jets

In a previous study we investigated three-scalar mixing in a turbulent coaxial jet (Caiet al.J. Fluid Mech., vol. 685, 2011, pp. 495–531). In this flow a centre jet and a co-flow are separated by an annular flow; therefore, the resulting mixing process approximates that in a turbulent non-premixed flame. In the present study, we investigate the effects of the velocity and length scale ratios of the annular flow to the centre jet, which determine the relative mean shear rates between the streams and the degree of separation between the centre jet and the co-flow, respectively. Simultaneous planar laser-induced fluorescence and Rayleigh scattering are employed to obtain the mass fractions of the centre jet scalar (acetone-doped air) and the annular flow scalar (ethylene). The results show that varying the velocity ratio and the annulus width modifies the scalar fields through mean-flow advection, turbulent transport and small-scale mixing. While the evolution of the mean scalar profiles is dominated by the mean-flow advection, the shape of the joint probability density function (JPDF) was found to be largely determined by the turbulent transport and molecular diffusion. Increasing the velocity ratio results in stronger turbulent transport, making the initial scalar evolution faster. However, further downstream the evolution is delayed due to slower small-scale mixing. The JPDF for the higher velocity ratio cases is bimodal at some locations while it is always unimodal for the lower velocity ratio cases. Increasing the annulus width delays the progression of mixing, and makes the effects of the velocity ratio more pronounced. For all cases the diffusion velocity streamlines in the scalar space representing the effects of molecular diffusion generally converge quickly to a curved manifold, whose curvature is reduced as mixing progresses. The curvature of the manifold increases significantly with the velocity and length scale ratios. Predicting the observed mixing path along the manifold as well as its dependence on the velocity and length scale ratios presents a challenge for mixing models. The results in the present study have implications for understanding and modelling multiscalar mixing in turbulent reactive flows.

Shear improved Smagorinsky model for large eddy simulation of flow in a stirred tank with a Rushton disk turbine

Large eddy simulation (LES) is a very attractive method for simulations of reactive flows for a wide range of Reynolds number. In this approach, the effects observed at the large scales (for velocity and concentrations) are directly computed using modelled interactions with the small subgrid scales. Small scales tend to be more isotropic than the large ones, so it is easier to predict their behaviour using simpler and more universal models than RANS ones and called subgrid-scale (SGS) models. In this work, computational fluid dynamics (CFD) and particle image velocimetry (PIV) techniques have been used to describe the flow field in standard stirred tank equipped with a Rushton disk turbine (RDT). A new efficient and cost effective SGS model called shear improved Smagorinsky model (SISM) for large eddy simulation (LES) has been successfully implemented and validated in the open source CFD code “OpenFOAM”. The shear improved Smagorinsky model is capable of predicting turbulent near wall region accurately without any wall function. The model is based on results concerning mean-shear effects in wall-bounded turbulence. It takes into account the mean shear arising due to anisotropy of the flow. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost when compared to the original Smagorinsky model and possesses a high potential for generalisation to complex non-homogeneous turbulent flows since no geometrical argument enters in the definition of the eddy-viscosity. However, an appropriate average must be specified in the absence of homogeneity directions. For this purpose we use an adaptive Kalman filter. There was good agreement between the CFD simulations and PIV experimental results.

Effects of mean shear on the local turbulent entrainment process

AbstractWe report on effects of mean shear on the turbulent entrainment process, focusing in particular on their relation to small-scale processes in the proximity of the turbulent/non-turbulent interface (TNTI). Three-dimensional particle tracking velocimetry (3D-PTV) measurements of an axisymmetric jet are compared to data from a direct numerical simulation (DNS) of a zero-mean-shear (ZMS) flow. First, conditional statistics relative to the interface position are investigated in a pseudo-Eulerian view (i.e. in a fixed frame relative to the interface position) and in a Lagrangian view. We find that in a pseudo-Eulerian frame of reference, both vorticity fluctuations and mean shear contribute to the vorticity jump at the boundary between irrotational and turbulent regions. In contrast, the Lagrangian evolution of enstrophy along trajectories crossing the entrainment interface is almost exclusively dominated by vorticity fluctuations, at least during the first Kolmogorov time scales after passing the interface. A mapping between distance to the instantaneous interface versus conditional time along the trajectory shows that entraining particles remain initially close to the TNTI and therefore attain lower average enstrophy values. The ratio between the rate of change of enstrophy in the two frames of references defines the local entrainment velocity ${v}_{n} = - (\mathrm{D} {\omega }^{2} / \mathrm{D} t)/ (\partial {\omega }^{2} / \partial {\hat {x} }_{n} )$, where ${\omega }^{2} $ is enstrophy and ${\hat {x} }_{n} $ is the coordinate normal to the TNTI. The quantity ${v}_{n} $ is decomposed into mean and fluctuating components and it is found that mean shear enhances the local entrainment velocity via inviscid and viscous effects. Further, the analysis substantiates that for all investigated flow configurations the local entrainment velocity depends considerably on the geometrical shape of the interface. Depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, i.e. viscous effects for convex shapes and vortex stretching for concave shapes, looking from the turbulent region towards the convoluted boundary. Moreover, turbulent fluctuations display a stronger dependence on the shape of the interface than mean shear effects.

Scalar fluctuations from a point source in a turbulent boundary layer

The downstream development of the concentration probability distribution along the mean-plume centerline of a dispersing plume in the wake of a ground-level continuous point source in a neutrally stratified wall-shear layer is studied. It is shown that the concentration distribution is well described by a family of one-parameter gamma distributions, as first suggested by Villermaux and Duplat [Phys. Rev. Lett. 91, 184501 (2003)] in the context of confined mixing. A prediction of the downstream evolution of the parameter k (which specifies the gamma distribution) is obtained. This prediction includes explicitly the effects of mean shear on the mean-square concentration.

Multimode stretched spiral vortex and nonequilibrium energy spectrum in homogeneous shear flow turbulence

The stretched spiral vortex [T. S. Lundgren, “Strained spiral vortex model for turbulent structures,” Phys. Fluids 25, 2193 (1982)] is identified in turbulence in homogeneous shear flow and the spectral properties of this flow are studied using direct-numerical simulation data. The effects of mean shear on the genesis, growth, and annihilation processes of the spiral vortex are elucidated, and the role of the spiral vortex in the generation of turbulence is shown. As in homogeneous isotropic turbulence [K. Horiuti and T. Fujisawa, “The multi mode stretched spiral vortex in homogeneous isotropic turbulence,” J. Fluid Mech. 595, 341 (2008)], multimodes of the spiral vortex are extracted. Two symmetric modes of configurations with regard to the vorticity alignment along the vortex tube in the core region and dual vortex sheets spiraling around the tube are often educed. One of the two symmetric modes is created by a conventional rolling-up of a single spanwise shear layer. Another one is created by the convergence of the recirculating flow or streamwise roll [F. Waleffe, “Homotopy of exact coherent structures in plane shear flows,” Phys. Fluids 15, 1517 (2003)] caused by the upward and downward motions associated with the streaks. The vortex tube is formed by axial straining and lowering of pressure in the recirculating region. The spanwise shear layers are entrained by the tube and they form spiral turns. The latter symmetric mode tends to be transformed into the former mode with lapse of time due to the action of the pressure Hessian term. The power law in the inertial subrange energy spectrum is studied. The base steady spectrum fits the equilibrium Kolmogorov −5/3 spectrum, to which a nonequilibrium component induced by the fluctuation of the dissipation rate ε is added. This component is extracted using the conditional sampling on ε, and it is shown that it fits the −7/3 power in accordance with the statistical theory. The correlation between these spectra and the appearance and diminution of the streaks and the two modes of the spiral vortex is discussed. The temporal variations of the spectrum are divided into two regimes, Phases 1 and 2. Large energy contained in the low-wavenumber range in Phase 1 is cascaded to the small scales in Phase 2. This energy transfer is accomplished by the reversal in the sign of −7/3 power component.

Equilibration of weakly nonlinear salt fingers

An analytical model is developed to explain the equilibration mechanism of the salt finger instability in unbounded temperature and salinity gradients. The theory is based on the weakly nonlinear asymptotic expansion about the point of marginal instability. The proposed solutions attribute equilibration of salt fingers to a combination of two processes: (i) the triad interaction and (ii) spontaneous development of the mean vertical shear. The non-resonant triad interactions control the equilibration of linear growth for moderate and large values of Prandtl number (Pr) and for slightly unstable parameters. For small Pr and/or rigorous instabilities, the mean shear effects become essential. It is shown that, individually, neither the mean field nor the triad interaction models can accurately describe the equilibrium patterns of salt fingers in all regions of the parameter space. Therefore, we propose a new hybrid model, which represents both stabilizing effects in a single framework. The resulting solutions agree with the fully nonlinear numerical simulations over a wide range of governing parameters.

Asymptotic expressions for the directivity of round jets

Expressions for the directivity of round jets, in the high and low frequency limits, are derived, based on solutions of Lilley's equations. Two different forms of the equation in what concerns source terms representation are considered, along with general point sources of the appropriate type (i.e., equivalent stress and force sources and also, when necessary, volume sources), which are assumed to be statistically axisymmetric. Effects of mean shear and temperature gradients are accounted for, as well as of source movement. The expressions are compared with earlier ones, based on a plug flow model. The differences in the resulting expressions due to the choice of source description, which are relevant for hot jets, are discussed and used to derive a form consistent with both representations. Comparison with experimental data is also presented.

Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows

A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified asvT=(Csδ)2(|S|—|〈S〉|): the magnitude of the mean shear |〈S〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor |S|;CSis the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbersReτ= 395 andReτ= 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.

Scaling of the near-wall layer beneath turbulent separated flow

This paper is a continuation of an earlier paper [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438] in which it is proposed that each Reynolds stress has its own velocity scale. Two of these, u τ ′ and w τ ′ , are directly related by definition to the r.m.s. of the wall-shear-stress fluctuations ( τ x and τ z ) in the streamwise and transverse directions. They are also velocity scales for the true dissipation of the turbulent kinetic energy and the Kolmogorov velocity and length scales at the surface. From asymptotic considerations it is shown that the other two scales are related to averages involving instantaneous gradients of wall-shear-stress fluctuations. The measurements, made using pulsed-wire anemometry into the viscous sublayer, show that u τ ′ and w τ ′ are also the velocity scales for the respective streamwise and transverse fourth-order velocity moments, together with the viscous velocity scale ( ν / y ). Normalised, the fourth-order moments show an inner-layer-like behaviour independent of both position and direction, like that seen in the second-order moments [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438]. However, not surprisingly, the third order moments exhibit an effect of mean shear, seen in the skewing of the probability distributions. Though not measured directly, the measurements imply the behaviour of the averaged products of fluctuations in wall-shear-stress and wall-pressure-gradient ( τ x ∂ p / ∂ x ¯ and τ z ∂ p / ∂ z ¯ ). Normalised, they also are independent of position and direction. Some of the results presented apply more generally to the near-wall region beneath turbulent flow.

On the Propagation of Baroclinic Waves in the General Circulation

The propagation of long, first mode, baroclinic planetary waves in eddy-resolving quasigeostrophic general circulation models is studied. Recent TOPEX/Poseidon observations argue oceanic first-mode planetary waves move with speeds other than those predicted by simple theory. These data have prompted theoretical analyses of wave propagation in a mean flow, with the results suggesting mean shear can have a controlling effect on the planetary wave guide. Some of the predicted effects appear to be relevant to the observations, while others are less obvious. This, coupled with other explanations for the observations, motivates the calculations. Based on these experiments, the authors suggest that the predicted effects of mean shear on wave propagation are consistent with those computed in a fully geostrophically turbulent ocean. These are that a two-layer model misses the dominant component of long-wave interaction with a mean flow, a three-layer model captures this interaction qualitatively, and the correction to wave propagation is in the direction opposite to the mean flow. Quantitative comparisons between the theory and the numerical experiments are good in the northern latitudes and questionable in the southern latitudes. Reasons for the southern discrepancy are offered.

Computation of Acoustic Propagation in Two-Dimensional Sheared Ducted Flows

Most aeroacoustic noise-prediction methods rely on an acoustic analogy featuring a propagation equation associated with source terms. These models were mainly applied to computation of acoustic far fields radiated by simple free flows like jets. The assumption is made in many formulations that the radiated acoustic field is not perturbed by the shear flow giving rise to the noise sources. These acoustic analogies thus do not provide a full description of acoustic/flow interactions. The Lilley equation was introduced to account, to a certain extent, for mean shear effects on propagation. More recently, this problem has been treated by making use of the linearized Euler equations, which are more flexible and more adequate for numerical simulations. As several types of modes are supported by the Euler equations, problems linked to their coupling have to be considered. It is then necessary to investigate acoustic field computations in complex flows. Our aim in the present article is to validate the wave operator associated with linearized Euler equations. Numerical tests deal with propagation in two-dimensional sheared ducted flows. Results are compared with other solutions deduced from analytical developments and direct numerical simulations. This study shows that the linearized Euler operator may be used to account for mean effects on wave propagation in the presence of sheared ducted flows. Processes that are specifically considered are 1) convection effects on axial disturbances, 2) refraction effects on oblique wave generation, and 3) source radiation effects on propagation in sheared flows.

Development of a turbulence model based on the energy spectrum for flows involving rotation

A generalized eddy viscosity model is formulated by using the rotation modified energy spectrum. Rotation and mean shear effects are directly included in the eddy viscosity without the use of the local equilibrium assumption. The formulation also includes the modeling of vortex stretching and viscous destruction terms of the dissipation rate equation based on the limit of rotating isotropic turbulence at high Reynolds numbers. The rotation modified energy spectrum includes the contribution of rotation effects on the dissipation and structure of turbulence. The model is shown to reproduce the dominant effects of rotation on turbulence in rotating homogeneous shear flows and turbulent channel flows subject to spanwise rotation. The general applicability of the model and its implications are also addressed.

Effects of Mean Shear on Momentum and Heat Transfer Processes.

Direct numerical simulations are performed to investigate the effects of mean shear and mean temperature gradient on the structure of homogeneous turbulence and related heat transport. First, homogeneously sheared turbulence with mean temperature gradient is evolved from the initial condition of isotropic turbulence. After the flow becomes fully developed, the mean shear and temperature gradient are removed and the succeeding return-to-isotropy process is examined in detail. It is found that the removal of mean shear gravely affects the decaying processes of turbulent shear stress and heat flux. In the spectral energy balance of Reynolds shear stress and hear flux, the non-linear term is found to transfer energy from high to low wave-numbers, thus indicating the counter-gradient transfer of heat and momentum occurs at high wave-numbers. And the visualization of instantaneous structures reveal that the counter-gradient transfer is uniquely associated with the longitudinal vortex tubes.